Incumbent Frankfort Mayor Bill May was prohibited from seeking a four-consecutive term in 2008 due to term limits.[3] Graham became the first person to enter the race to succeed May, announcing his candidacy on November 9, 2007.[3] Graham defeated opponent Lynn Bowers, a city commissioner, in the Frankfort mayoral election in November 2008.

Graham declined to seek re-election in 2012 after one, four-year term.[4] Graham told The State Journalnewspaper on January 25, 2012, ""I have no intentions of re-filing for election. I've known for sometime I'm not going to run...The people of Franklin County have always been good to me. Anytime I've been on the ballot, I've received the highest amount of votes and I've served the best way I know how."[4] The election to succeed him will be held in November 2012.